Question

What does the exponent of the regression coeffcient, exp(B), represent in a logistic regression model?

Answer 1

let a linear regression equation be

y=b₀+b₁x₁+b₂x₂+.....................b_kx_k   .

Linear regression is based on Least Square estimates where Logistic regression is based on Maximum Likelihood Estimate such that it maximises the probaility of Y given X(likelihood).

The logistic Regression equation

Logit(p)=b₀+b₁x₁+b₂x₂+.....................+b_kx_k  

Where Logit(p)=Log(p/1-p)

(p=probability of the dependent variable equalling a "succcess" or "event")

Taking exponential boththe sides of

Logit(p)=b₀+b₁x₁+b₂x₂+.....................+b_kx_k   we get

Tis is how the exponent of the regression coeffcient, exp(B), represent in a logistic regression model